Genesis /ALICE Benchmarking
Igor Zagorodnov
Beam Dynamics Group Meeting
17.03.08
Genesis 1.3(S.Reiche et al)
ALICE
• only 3D • 3D Cartesian field solver (ADI)• Runge-Kutta integrator• Dirichlet boundary conditions• transverse motion• many other physics• parallel (MPI)
• 1D/2D/3D • 3D azimuthal field solver (Neumann)• Leap-Frog integrator• Perfectly Matched Layer• transverse motion• simplified model• parallel (MPI)• tested by me on the examples from the book of SSY
(~Saldin et al, 2000 „The Physics …“,)
2.5 MeV
100 150 2000
0.5
1
1.5
2x 10
10[GW]P
[m]z
2.5MeVE
0C 4.086e-5 mr
Genesis vs. ALICE / Energy Spread (round Gaussian beam, Gaussian energy spread, parallel motion only)
ALICE
Genesis
W = 4 kW
SASE 2 parameters
0.1 nms
How to simulate emmitance with laminar particle motion only?
22
2 20
ˆT
4 2
2 02 2
ˆ zemit
2 2 2,
ˆ ˆ ˆT eff T emita
1
4a -E. Saldin et al, TESLA-FEL 95-02 (1995);
S.Reiche PhD Thesis (1999).
1a - E. Saldin et al, The Physics of Free Electron Lasers (2000)
2a - E. Saldin et al, DESY 05-164 (2005)
100 150 2000
2
4
6
8
10
12
14
16x 10
9
[W]P
[m]z
0C
4.4038e-005mr
Genesis vs. ALICE / Emmitance(round Gaussian beam, Gaussian energy spread)
47.44m
1MeVE
3MeV
4MeV
5MeV
ALICE (laminar)
Genesis
1MeVE 1.4 mm×mradn
1.4 mm×mradn
0 0.2 0.4 0.6 0.8 1 1.20.057
0.058
0.059
0.06
0.061
0.062
0.063
1.1a
ALICE (laminar)
Genesis
ˆdetuning C
Field growth rate
Genesis vs. ALICE (emittance parameter fit)
0 50 100 150 20010
-6
10-4
10-2
100
102
100 120 140 160 180 2000
5
10
15
20
25
1.1a
ALICE (laminar)
Genesis
[ W]P G
[m]z [m]z
[ W]P G
Detuning corresponds to maximal growth rate in linear regime
0( ) maxC
C
Genesis vs. ALICE with laminar motion
The transverse motion has to be implemented in ALICE
Genesis vs. ALICEwith transverse motion
2.5MeVE
0C P0 = 4 kW
100 150 2000
1
2
3
4
19%Genesis (N=6e4)Genesis (N=3e4)
Alice (N=6e4)
Alice (N=3e4)
The difference in saturation length is 7 %.The difference in power gain is 19 %.
The difference does not reduce with changing of the discrete model parameters ?!.
4.086e-5 mr
[m]z
[ W]P G
I=5KAN ~10 400
0.1 nms
GINGER/GENESIS results for “0-order” 200-
pC case
Observations:• Again, GENESIS shows slightly longer
gain length, 10-m later saturation but 15% higher power
• Again, GINGER shows deeper post-saturation power oscillation
• Little sensitivity (2 m, 7%) in GINGER results to 8X particle number increase
• Possible reasons for differences: bugs slight differences in initial e-beam
properties (e.g. mismatch) grid effects (e.g. outer boundary)???
William M. Fawley, ICFA 2003 Workshop on Start-to-End Numerical Simulations of X-RAY FEL’s
Bridsall C.K., Langdon A.B., Plasma Physics via Computer Simulations, 1991Dawson J.M, Particle simulation of Plasmas // Reviews of Modern Physics, 1983
About advantages of the „quiet start“ see, for example, in
4 23
Ntrans x,
%
y,
%
px,
%
py,
%
Genesis
7500 1.5 7.5 5.1 5.8
15000 4.1 4.7 4.1 3.2
ASTRA
7500 1.6 4.2 0.43 2.3
15000 0.4 3.3 0.62 1.9
Alice
7500 0.8 1.0 0.8 0.8
15000 0.4 0.4 0.5 0.5
4 4
4100%
Properties of the Normal macroparticle distribution
Ntrans Rxy Rpxpy Rxpy Rypx
Genesis
7500 8e-3 2e-2 5e-3 8e-3
15000 8e-3 1e-2 1e-3 3e-3
ASTRA
7500 4e-3 7e-3 5e-3 5e-3
15000 5e-3 4e-3 6e-3 4e-3
Alice
7500 1e-3 2e-3 8e-4 2e-3
15000 5e-4 1e-3 5e-4 8e-4
cov( , )R
Properties of the Normal macroparticle distribution
-4 -2 0 2 40
100
200
300
400
500
600
700
-4 -2 0 2 40
100
200
300
400
500
600
700ALICE Genesis
7500transN
/ yy / yy
4* transn N
clustering
Quiet start ?
What is the reason?
-4 -2 0 2 40
50
100
150
4* transn NtransN
/ yy
ASTRA
The polar form of Box-Muller algorithm (in Genesis) maps the „quiet“ uniform distribution in a clustered normal distribution.
UniformNormal
Quiet start ?
ALICE Genesis
2000transN / rx
/ ry
Quiet start ?
clusteringr x y
ALICE Genesis
2000transN
/rx pp
/ry pp
Quiet start ?
clustering
r x yp p p
-4 -2 0 2 4-4
-3
-2
-1
0
1
2
3
4
ASTRA
2000transN /
rx pp
/ry pp
r x yp p p
100 150 2000
0.5
1
1.5
2
2.5
3[ W]P G
[m]z
Modified Genesis vs. ALICEwith transverse motion
2.5MeVE
0C P0 = 4000 Watt
Genesis(modified) (N=6e4) Alice (N=6e4)
The transformation used in ALICE
12 erf (2 1)i iY X
It transforms the uniform distribution Xi (0,1) to the normal distribution Yi ().This transformation does not destroy the „quiet start“.
It uses the straightforward transformation by inverse error function
Convergence
104
105
2.5
2.7
2.9
3.1
3.3
3.53.5
104
105
106
0
2
4
6
8
10
12
[ W]P G4 4
4100%
Genesis
Genesis (modified)
ALICE
Genesis
Genesis (modified)
ALICE4* transn N 4* transn N
Genesis: Hammersley and Box-MuellerGenesis (modified): Hammersley and the inverse error functionALICE: Sobol and the inverse error function
2.5MeVE 0C I=5KA
N ~10 4000.1 nms
at saturation